Abstract The Sinh–Poisson equation and the RLC transmission line equation are important nonlinear model equations in the field of engineering and power transmission. The modified simple equation (MSE) procedure is a realistic, competent and efficient mathematical scheme to ascertain the analytic soliton solutions to nonlinear evolution equations (NLEEs). In the present article, the MSE approach is put forward and exploited to establish wave solutions to the previously referred NLEEs and accomplish analytical broad-ranging solutions associated with parameters. Whenever parameters are assigned definite values, diverse types of solitons originated from the general wave solutions. The solitons are explained by sketching three-dimensional and two-dimensional graphs, and their physical significance is clearly stated. The profiles of the attained solutions assimilate compacton, bell-shaped soliton, peakon, kink, singular periodic, periodic soliton and singular kink-type soliton. The outcomes assert that the MSE scheme is an advance, convincing and rigorous scheme to bring out soliton solutions. The solutions obtained may significantly contribute to the areas of science and engineering.

中文翻译：

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数学物理中非线性 RLC 传输线方程和 Sinh-Poisson 方程的稳定解

摘要 Sinh-Poisson方程和RLC传输线方程是工程和电力传输领域中重要的非线性模型方程。修正的简单方程 (MSE) 程序是一种现实的、称职的和有效的数学方案，用于确定非线性演化方程 (NLEE) 的解析孤子解。在本文中，MSE 方法被提出并被用于为先前提到的 NLEE 建立波解，并完成与参数相关的广泛解析解。每当参数被赋予确定的值时，各种类型的孤子都来自一般的波解。通过绘制三维和二维图形来解释孤子，并清楚地说明了它们的物理意义。所得解的轮廓同化了压实子、钟形孤子、峰子、扭结、奇异周期、周期孤子和奇异扭结型孤子。结果表明，MSE 方案是一种先进的、令人信服的和严格的方案，可以提供孤子解决方案。获得的解决方案可能会对科学和工程领域做出重大贡献。